Session 3220 Teaching DSP: Bridging the Gap from Theory to Real-Time Hardware Cameron H. G. Wright Department of Electrical Engineering U.S. Air Force Academy, CO Thad B. Welch, Delores M. Etter Department of Electrical Engineering U.S. Naval Academy, MD Michael G. Morrow Department of Electrical and Computer Engineering University of Wisconsin-Madison, WI Abstract Many digital signal processing (DSP) topics are difficult for undergraduates to internalize, but studies have shown that demonstrations and laboratory experiences can facilitate the process. In the past, many barriers prevented including real-time DSP hardware in an undergraduate curriculum. This paper describes a pedagogical model the authors have developed which includes theory, demos, lab exercises, and real- time DSP experience using Matlab, C, and real-time DSP hardware that overcomes the barriers. This model has been very successful. 1 Introduction A common complaint heard from electrical engineering (EE) undergraduates is that many (if not most) of the EE topics are difficult to visualize. One of the fastest growing fields in EE, digital signal processing (DSP) certainly has more than its share of concepts that fit this description. In particular, making the leap from Matlab DSP simulations to real-time DSP hardware has proven to be singularly challenging for faculty and students alike. It is well known that demonstrations and laboratory experiences help most students internalize both the theoretical underpinnings and the practical ramifications of various DSP topics, 1–3 but real-time DSP hardware and software have usually been considered too difficult for undergraduates. This high degree of difficulty is due to many factors, including the need to understand parallel processing, multiple memory busses, specialized instruction sets, and— most importantly—a lack of documentation that is “readable” by the non-expert. Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright c 2002, American Society for Engineering Education Page 7.1069.1
Transcript
Session 3220
Teaching DSP: Bridging the Gap
from Theory to Real-Time Hardware
Cameron H. G. WrightDepartment of Electrical Engineering
U.S. Air Force Academy, CO
Thad B. Welch, Delores M. EtterDepartment of Electrical Engineering
U.S. Naval Academy, MD
Michael G. MorrowDepartment of Electrical and Computer Engineering
University of Wisconsin-Madison, WI
Abstract
Many digital signal processing (DSP) topics are difficult for undergraduates tointernalize, but studies have shown that demonstrations and laboratory experiencescan facilitate the process. In the past, many barriers prevented including real-timeDSP hardware in an undergraduate curriculum. This paper describes a pedagogicalmodel the authors have developed which includes theory, demos, lab exercises, and real-time DSP experience using Matlab, C, and real-time DSP hardware that overcomesthe barriers. This model has been very successful.
1 Introduction
A common complaint heard from electrical engineering (EE) undergraduates is that many(if not most) of the EE topics are difficult to visualize. One of the fastest growing fields inEE, digital signal processing (DSP) certainly has more than its share of concepts that fitthis description. In particular, making the leap from Matlab DSP simulations to real-timeDSP hardware has proven to be singularly challenging for faculty and students alike. It iswell known that demonstrations and laboratory experiences help most students internalizeboth the theoretical underpinnings and the practical ramifications of various DSP topics,1–3
but real-time DSP hardware and software have usually been considered too difficult forundergraduates. This high degree of difficulty is due to many factors, including the need tounderstand parallel processing, multiple memory busses, specialized instruction sets, and—most importantly—a lack of documentation that is “readable” by the non-expert.
Figure 1: A systematic model for teaching DSP. The last two steps can be iterated asneeded.
Over the last few years, we have developed a systematic method to teach DSP to undergrad-uates. It provides students with a firm bridge from their first exposure to theory all the wayto practical implementation of real-time DSP code on industry-standard hardware, such asthe Texas Instruments (TI) C6711 digital signal processing starter kit (DSK). Previous ar-ticles4–11 have described the application of this method to specific DSP concepts; this articlegeneralizes the lessons learned and outlines the overall method in such a way that it couldbe applied to any DSP topic. A world wide web URL is provided at the end of this articlefor downloading the software that is a key component of our method for “bridging the gap”from theory to real-time hardware.
2 A Graduated Approach to Teaching DSP
2.1 Using a “Bridge” to Real-Time
A systematic model for teaching DSP is shown graphically in Figure 1. It begins withthe traditional presentation of the theory behind each new topic, followed by a specificprogression of exercises.
To facilitate the learning process in a DSP class, demonstrations of fundamental topics arehelpful supplements to the theory. In particular, computer-based demonstrations are highlyeffective for a student’s initial grasp of a new DSP topic; this is reflected in the contentof many newer DSP texts.12–17 We take advantage of the fact that the software packageMatlab18 and its related toolboxes have become a mainstay in most EE programs. Givenour students’ familiarity with Matlab, computer exercises that implement DSP theory area natural approach. However, today’s students are quickly bored with a “canned demo,”and the application of these demonstrations to real-time DSP is limited. In response we havecreated a series of interactive demos that allow the student to “play” with a concept andengage in “what if?” explorations, while laying the foundation for real-time applications.
Such interactive demonstrations typically result in much greater comprehension of the topicby the student, yet we have found that taking the next step of requiring the student toprogram an example of the concept in Matlab is needed to solidify the student’s under-standing. DSP programming has long been used in graduate-level DSP classes, but has onlyrecently been applied to undergraduates. When the student can comfortably create a basicMatlab program that performs a particular DSP operation (such as FIR filtering) on stored
data, then we can start to ease them into real-time DSP.
Moving beyond a Matlab-only program to a real-time hardware implementation is highlydesirable from a pedagogical point of view. Many practical issues and learning opportunitiesoccur only when the students try to adapt their newly acquired knowledge to the challenge ofreal-time DSP. For example, interrupt-driven processing, tradeoffs of on-chip versus off-chipmemory access, and utilization of specific hardware capabilities are all issues that arise onlywhen the DSP operation is implemented in real-time hardware. In the past, this next stepin understanding has been impeded by a very abrupt transition, in terms of cost to equip astudent laboratory and in terms of the steep learning curve (for both students and faculty) ofunfamiliar systems and software. We therefore developed a software and hardware “bridge”between Matlab and real-time DSP hardware that makes it possible to smoothly andincrementally transition from the Matlab-only domain to a full hardware implementationoperating in real-time, while retaining as needed the impressive capabilities of the Matlabdisplay engine. Using this approach, students are able to develop and enhance their ownreal-time DSP programs in an iterative way, “moving” more and more of their code fromthe realm of Matlab over to C or assembly language for the DSK. The last two steps ofFigure 1 illustrate this iterative nature of the model.
2.2 Choosing the DSP Hardware
As detailed in previous articles, we chose to construct our DSP educational platform aroundMatlab and the TI C6x DSK. The current version of the TI C6x DSK makes use of theVLIW architecture TMS320C6711 microprocessor and includes 16 MB of memory, basicsupport circuitry, and excellent software development tools (Code Composer Studio) thatinclude an optimizing C compiler, debugger, assembler, and linker. This meets our criteria oflow cost, sufficient processing power, ample memory, and a versatile software developmentenvironment. Furthermore, while other companies such as Analog Devices and Motorolaalso manufacture DSP microprocessors, we have been unable over the years to elicit interestfrom any other company in the educational segment; only TI has consistently demonstratedsuch interest. See reference [19] for details on this DSK, and see reference [20] for moreinformation on TI DSP products and support in general.
Unfortunately, to keep costs down, the native codec on the C6711 DSK board is the TITLC320AD535 chip, a single-channel telephone-quality device with a maximum samplingfrequency of only fs ≈ 8 kHz. This severely limits the utility of the DSK for a variety ofDSP applications we desire for our students. However, we feel the DSK’s advantages out-weigh this disadvantage, and the inclusion of a flexible Expansion Daughter Card Interfaceon the DSK allows us to circumvent this limitation quite easily. We supplement the basicDSK as needed for a particular application with more capable I/O such as a CD-qualitystereo codec board21 or a high speed multichannel ADC.9,11 These small daughter cards areavailable to the public at very low prices; see reference [22] for more information. Using theC6711 DSK and the appropriate daughter card as the core, a professor can populate a highlyflexible real-time DSP student laboratory at low cost.
One of the primary choices in practical DSP hardware today is the question of floating-pointversus fixed-point implementations.23 While the floating-point ability of the TI C6711 DSKoffers a pedagogical advantage (topics such as scaling and overflow may be postponed untillater), the C6711 processor can also run fixed-point code if the professor desires. This “twofor the price of one” ability represents another strong advantage of the C6711 DSK, in ouropinion.
3 Examples Of Using The Model
To clarify the use of this teaching model, we describe three examples of DSP topics thathave benefitted from this approach: basic FIR filter design, an application of a particulartype of FIR filter (the Hilbert transformer) for communications systems, and audio specialeffects (flanging and chorus).
3.1 FIR Filter Design
One of the first “theory to real-time implementation” labs that our students experience isthe design of an FIR filter. Our students learn the basic theory first, such as the generalizedtransfer function given by
H(z) =M∑i=0
h[i]z−i (1)
where M is the filter order and h[i] is the ith coefficient of the filter’s impulse response.24
We use interactive demos, based first upon the sptool GUI provided with Matlab’s SignalProcessing Toolbox shown in Figure 2. Students are encouraged to use sptool to createFIR filter designs, but also introduced to the underlying programs such as remez whichcan produce filters sptool cannot. Next, we move them to a program we designed calledqfilt (see Figure 3) which serves several purposes.6 The qfilt program allows studentsto understand the ramifications of issues such as coefficient quantization and realizationtradeoffs, but also provides a bridge to real-time DSP. Note the button labelled Load/RunDSK (on the right, fifth button from the bottom). Clicking this button takes the filtercoefficients the student has produced, loads an FIR filter routine on the DSK that implementsthis design, and runs the DSK in real-time to demonstrate the filtering effect. This getsthe student past the initial fear of dealing with real-time DSP hardware. It is amazinghow profound an effect can be observed in most students who listen for the first time tothe sound produced by a real-time DSP filter that they designed themselves! After thisexperience, we move the student toward creating their own code in C for the DSK usingthe Code Composer Studio software tools which come with the DSK, shown in Figure 4.
Eventually the student creates a working “brute force” FIR filter that runs on the DSK. Weprovide helper programs for Matlab which format filter coefficients created in Matlabinto an “include” file that can be easily used by a C program. We encourage the studentto further refine the C program, implementing, for example, circular buffering. Before long,the student is almost effortlessly validating filter designs in Matlab, then moving them tothe DSK using C.
3.2 Using the Hilbert Transformer
Once our students have mastered the basic implementation issues associated with FIR filters,a real-world application is needed. For our example here, we have selected a DSP-basedenvelope detector for a communications system receiver. This type of detector can be usedto recover the message associated with a commercial amplitude modulation (AM) signal. Abrief review of the theory follows.
The expression for a double-sideband (with carrier) AM signal is,
sAM(t) = Ac[1 + m(t)] cos(ωct) (2)
In this equation, Ac is the amplitude of the carrier, m(t) is the message signal (with amplitude≤ 1 to prevent overmodulation), and ωc is the carrier frequency expressed in radians/sec.25
In order to recover the message signal, it is necessary to extract the envelope of the signalAc[1 + m(t)]. Once the envelope is obtained, the DC component can be removed with a DCblocking filter, leaving Acm(t), which is a scaled version of the original message signal.
The general principle of message recovery using DSP techniques is to select only the positive(or negative) frequency component of the signal∗ and determine its magnitude, which willbe proportional to the envelope.26 A Hilbert transformer filter will generate an all-pass 90◦
phase-shifted version of the received signal that is called the Q (for “quadrature”) compo-nent. The non-phase-shifted version of the received signal is called the I (for “in-phase”)component. Note that the analytic signal z(t), defined as
z(t) = I(t) + jQ(t) (3)
contains only positive frequency components. An important learning step for our studentsis to realize that they must account for the group delay of this FIR filter in order to alignthe I component with the Q component of the AM signal. At this point in the receiverdevelopment, the envelope may now be expressed as
envelope of sAM(t) =√
I2(t) + Q2(t) (4)
which means the envelope can be extracted using DSP techniques. The square root operationin Equation 4 may be directly implemented (for example using the floating point sqrtf
command available via the DSK’s C compiler) or by using a less computationally intensiveapproximation technique. As our teaching model suggests, the student first learns the theorywith the aid of interactive demos, then develops a working solution off-line in Matlab, theneventually moves to the DSK and implements a fully functional real-time DSP solution.
Example plots from a student project are shown in Figures 5–7. The AM signal shown inFigure 5 is a 2 kHz carrier modulated by a 700 Hz sinusoidal message signal. Note: in anactual software radio this would be the IF output. Figure 6 shows the impulse response ofthe Type III FIR filter the student designed using Matlab’s remez program to implementa Hilbert transformer on the DSK. A comparison of the original message and the recoveredmessage using this DSP technique is shown in Figure 7. Note how well this design works!
We observe significant excitement and enthusiasm of our students when they can see real-time DSP-based demodulation working as a result of their own design.
∗Recall that a real sinusoidal signal made up of positive and negative frequency components can bethought of as two counterrotating vectors; a complex sinusoidal signal, sometimes called an analytic signal,is made up of only a positive or negative frequency component and can be thought of as a single rotatingvector. Signals made up of multiple frequencies can be treated similarly.
Figure 7: A comparison of the original message signal with the signal demodulated via DSP.
3.3 Audio Special Effects: Flanging and Chorus
An area of DSP in which many students are very interested is audio special effects. Alteringthe sound of an electric guitar or voice in real-time using student designed programs for theDSK has been extremely motivational for the students. We first describe to them the basictheory of special effects such as flanging and chorus, provide some demonstrations, thenchallenge the students to write algorithms in Matlab using stored sound files.
A block diagram of the flanging effect is shown in Figure 8, where α is a scale factor, andβ[n] is a periodically varying delay described by
β[n] =R
2(1 − cos (ω0n)) . (5)
In Equation 5, R is the number of sample-time delays and ω0 is a relatively low frequency.
A block diagram of the chorus effect is shown in Figure 9. To generate the chorus effect,three separately flanged signals are summed with the original signal. For a proper choruseffect, each of the βi and αi factors should be independent.
To ease the students on to the “bridge” that will get them to real-time processing, wefirst provide them with a custom program called winDSK6 which provides a highly flexiblegraphical user interface that can easily manipulate the C6711 DSK (see Figure 10).
The winDSK6 Audio Effects module contains a mixture of both FIR and IIR applications.
Clicking on the Audio Effects button from the winDSK6 main window will load the audioeffects program module into the attached DSK, and a window similar to Figure 11 willappear. The flanging and chorus effects are both implemented with FIR filters. Afterbecoming comfortable with their own Matlab programs and winDSK6, the next step is forthem to write similar programs of their own in C that will run in real-time on the DSK.
Audio special effects have been particularly popular as capstone senior design projects, wherethe student designs and builds a unit which typically contains a C6711 DSK, power supply,interface buffers/amplifiers for microphones and/or electric guitars, and various user controls.
Figure 11: The winDSK6 program running the Audio Effects application.
The unit produces whatever real-time audio special effect is created by the student’s software,such as flanging, chorus, echo, reverb, harmonic generation, etc. This project effectivelycombines hardware and software in a single capstone design experience. It should be notedthat until we implemented our “bridging the gap” method of teaching real-time DSP wecould not entice a single student to pursue such a senior design project; after implementingthe method there have been multiple students each year who enthusiastically chose such aproject.
4 Conclusions
We have developed a systematic teaching model that allows our students to firmly grasp newDSP topics, and to smoothly transition from theory to a real-time DSP system implemen-tation. Experiences at our respective institutions have shown that, compared to traditionalundergraduate DSP classes, this model promotes greater comprehension of the theoreticalunderpinnings as well as the practical ramifications of each new DSP topic. The hardwareinvestment required to implement such a model is rather modest, and much of the softwareneeded has already been developed by the authors.
We freely distribute much of the associated software for educational, non-profit use, andinvite user suggestions for improvement. See reference [27] for downloading the software;any interested parties are also invited to contact the authors via e-mail.†
References
[1] R. F. Kubichek, “Using Matlab in a speech and signal processing class,” in Proceedingsof the 1994 ASEE Annual Conference, pp. 1207–1210, June 1994.
[2] C. S. Burrus, “Teaching filter design using Matlab,” in Proceedings of the IEEE In-ternational Conference on Acoustics, Speech, and Signal Processing, pp. 20–30, Apr.1993.
[3] R. G. Jacquot, J. C. Hamann, J. W. Pierre, and R. F. Kubichek, “Teaching digital filterdesign using symbolic and numeric features of Matlab,” ASEE Comput. Educ. J.,vol. VII, pp. 8–11, January-March 1997.
†For those interested in a more in-depth treatment of this “bridging the gap” method, a new book isnearing completion. It will include a guided step-by-step mastery of real-time DSP concepts using the TIC6711 DSK, many detailed laboratory experiments, all required background information on hardware andsoftware issues for the C6711 DSK, and complete support software (Matlab, C, and assembly). Pleasecontact Dr. Welch for information on this book.
[4] C. H. G. Wright and T. B. Welch, “Teaching DSP concepts using Matlab and theTMS320C5X,” in Proceedings of the 1998 Texas Instruments DSP Educators and Third-Party Conference, (Houston, TX), August 6–8, 1998.
[5] C. H. G. Wright and T. B. Welch, “Teaching DSP concepts using Matlab and theTMS320C31 DSK,” in Proceedings of the IEEE International Conference on Acoustics,Speech, and Signal Processing, Mar. 1999. Paper 1778.
[6] C. H. G. Wright and T. B. Welch, “Teaching real-world DSP using Matlab,” ASEEComput. Educ. J., vol. IX, pp. 1–5, Jan–Mar 1999.
[7] M. G. Morrow, T. B. Welch, and C. H. G. Wright, “An inexpensive software tool forteaching real-time DSP,” in Proceedings of the 1st IEEE DSP in Education Workshop,(Hunt, TX), IEEE Signal Processing Society, Oct. 2000.
[8] T. B. Welch, C. H. G. Wright, and M. G. Morrow, “Poles and zeroes and Matlab, ohmy!,” ASEE Comput. Educ. J., vol. X, pp. 70–72, Apr. 2000.
[9] M. G. Morrow, T. B. Welch, C. H. G. Wright, and G. W. P. York, “Demonstration plat-form for real-time beamforming,” in Proceedings of the IEEE International Conferenceon Acoustics, Speech, and Signal Processing, May 2001. Paper 1146.
[10] M. G. Morrow, T. B. Welch, and C. H. Wright, “An introduction to hardware-based DSPusing winDSK6,” in Proceedings of the 2001 ASEE Annual Conference, (Albuquerque,NM), June 2001. Session 1320.
[11] G. W. York, M. G. Morrow, T. B. Welch, and C. H. Wright, “Teaching real-timesonar with the C6711 DSK and MATLAB,” in Proceedings of the 2001 ASEE AnnualConference, (Albuquerque, NM), June 2001. Session 1320.
[12] V. K. Ingle and J. G. Proakis, Digital Signal Processing Using Matlab V.4. BookwareCompanion Series, PWS Publishing, 1997.
[13] B. Porat, A Course in Digital Signal Processing. John Wiley & Sons, 1997.
[14] M. A. Yoder, J. H. McClellan, and R. W. Schafer, “Experiences in teaching DSP firstin the ECE curriculum,” in Proceedings of the 1997 ASEE Annual Conference, June1997. Paper 1220-06.
[15] A. Ambardar and C. Borghesani, Mastering DSP Concepts Using Matlab. PrenticeHall, 1998.
[16] S. K. Mitra, Digital Signal Processing: A Computer-Based Approach. McGraw-Hill,2nd ed., 2001.
[17] J. H. McClellan, C. S. Burrus, A. V. Oppenheim, T. W. Parks, R. W. Schafer, andS. W. Schuessler, Computer-Based Exercises for Signal Processing Using Matlab 5.Matlab Curriculum Series, Prentice Hall, 1998.
[18] The MathWorks, Inc., Natick, MA, MATLAB: The Language of Technical Computing,2000.
[20] Texas Instruments, Inc., “Digital signal processing,” 2001. http://dspvillage.ti.
com/.
[21] C. H. Wright, T. B. Welch, and M. G. Morrow, “Teaching transfer functions withMATLAB and real-time DSP,” in Proceedings of the 2001 ASEE Annual Conference,(Albuquerque, NM), June 2001. Session 1320.
[22] Educational DSP, L.L.C., “DSP resources for TI DSKs,” 2002. http://www.
educationaldsp.com/.
[23] C. Inacio and D. Ombres, “The DSP decision: Fixed point or floating?,” IEEE Spectrum,pp. 72–74, Sept. 1996.
[24] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing.Prentice Hall, 2nd ed., 1999.
[25] L. W. Couch, II, Digital and Analog Communication Systems. Prentice Hall, 6th ed.,2001.
[26] M. E. Frerking, Digital Signal Processing in Communication Systems. Van NostrandReinhold, 1994. 7th printing 2000 by Kluwer Academic Publishers.
[27] M. G. Morrow, “University of Wisconsin at Madison,” 2002. http://eceserv0.ece.
wisc.edu/~morrow/software/.
CAMERON H. G. WRIGHT, Ph.D, P.E., is a Professor and Deputy Department Head of the De-partment of Electrical Engineering at the U.S. Air Force Academy, Colorado Springs, CO. His researchinterests include signal and image processing, biomedical instrumentation, communications systems, andlaser/electro-optics applications. Lt. Colonel Wright is a member of ASEE, IEEE, SPIE, NSPE, Tau BetaPi, and Eta Kappa Nu. E-mail: [email protected]
THAD B. WELCH, Ph.D, P.E., is an Associate Professor in the Department of Electrical Engineering atthe U.S. Naval Academy, Annapolis, MD (from 1994–1997 he was an Assistant Professor in the Departmentof Electrical Engineering at the U.S. Air Force Academy). His research interests include multicarrier com-munication systems analysis and signal processing. Commander Welch is a member of ASEE, IEEE, andEta Kappa Nu. E-mail: [email protected]
DELORES M. ETTER, Ph.D, is a Professor in the Department of Electrical Engineering at the U.SNaval Academy, Annapolis, MD, and holds the ONR Distinguished Chair in Science and Technology. From1998–2001, she was the Deputy Under Secretary of Defense for Science and Technology. She is author ofa number of engineering textbooks and her research interests include adaptive signal processing. ProfessorEtter is member of the National Academy of Engineering, a Fellow of the IEEE and the ASEE, and a memberof Tau Beta Pi and Eta Kappa Nu. E-mail: [email protected]
MICHAEL G. MORROW, P.E., is a Faculty Associate in the Department of Electrical Engineering atthe University of Wisconsin, Madison, WI (from 1996–2000 he was a Master Instructor in the Department ofElectrical Engineering at the U.S. Naval Academy). His research interests include real-time digital systems,power system automation, and software engineering. He is a member of IEEE. E-mail: [email protected]
